This study deals with the real time coding and estimation of linear discrete time scalar system over communication networks. With the mean-squared error (MSE) distortion criterion, the information rate distortion function describing the performance limit of the coding-estimation system is analyzed and discussed. To achieve near instantaneous encoding and decoding, an asymptotic design scheme has been presented as a realization of real time coding-estimation system. The outputs of standard Kalman filter relying on unquantized observations are encoded using the Lloyd-Max quantization rules and transmitted over the noiseless channel. The decoder side runs the corresponding decoding and reconstruction algorithms to produce the optimal real time state estimate of system. To synchronize the encoder and decoder, a doublepredictor regime on the updating rules of the encoder-decoder pair is proposed, and it does not require any feedback information. The rate distortion function of the proposed scheme is derived and when comparing with the information theoretical lower bound, there is only a factor discrepancy related to the quantization rules. The rate distortion performance results of various design schemes are compared and demonstrated with numerical simulations. INDEX TERMS Real time coding and estimation, mean-squared error, information rate distortion function, Lloyd-Max quantization, double-predictor regime.

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Summary This paper investigates the schemes of asymptotically optimal quantization and bit allocation for distributed estimation in wireless sensor networks in which a total bit rate constraint is imposed. Because there is no communication among all sensors, quantizers for observations need to be designed separately. The Lloyd‐Max quantizer is shown to be asymptotically optimal for each sensor. Moreover, it is shown that the level number of asymptotically optimal quantization for sensors is proportional to the signal‐to‐noise ratio, which is determined by the variances of observation and noise. Because the original quantized minimum mean‐square error estimator often corresponds to a high computational cost when a large number of sensors are active, in our work, an asymptotically equivalent algorithm of iterative quantized estimator (IQE), which enjoys a low computational cost, is proposed. In addition, an IQE algorithm can be applied to wireless sensor networks with delay or packet loss. Simulation results of this work indicate that the effectiveness of our IQE algorithm is obvious; that is, a significant improvement of estimation performance is achieved by using the optimal bit allocation when comparing with the uniform bit allocation. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies the optimal rate allocation (ORA) problem for multi-sensor distributed estimation in wireless sensor networks (WSNs) where a total bit rate constraint is imposed. We adopt the mean-square error (MSE) as the the performance criterion of the designed distributed estimator, and search for the optimal rate allocation scheme through minimizing the upper bound of the designed estimator MSE. We consider the two-sensor case in WSN, and obtain a optimal rate allocation scheme, where the optimal bit rate of each sensor is basically determined by the local signal-to-noise ratio (SNR). Simulation results show that the optimal rate allocation scheme improves evidently on the simple uniform rate allocation scheme.